One problem I find in discussions, particularly internet discussions and most particularly those with a controversial topic, is that people will have a tendency to be dishonest. It is as though they are trying to score points with their base or something and not trying to convince the person who believes differently.
For example: Abortion supporters will chant “her body, her choice” as if it should make the wonderfulness of abortion self-evident. They refuse to admit that those of us who are opposed to abortion do not think the child is her body. Many of them will deny that we believe what we believe. Only too often you will see “oh, you only want to control women” or the term “anti-choice.” (There is a secondary consideration in that many supporters of abortion do not apply the concept of discretion over one’s own body to other topics — if they oppose recreational drug use or elective amputation. For these people, the mantra is false outright.)
The first indicator of what someone believes is what he says he believes. If you are going to declare outright that he is lying about his beliefs, you should first have evidence to that effect. You should be able to point to statements and/or actions that do not fit in with his stated beliefs. No, holding up your propaganda and saying it says he believes X when he says he believes Y does not count.